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Why do this problem?

This short problem is a reasonably routine application of kinematics; the interest lies in the numbers obtained and the questions concerning the validity of a physical model of constant gravitational force.

Possible approach

Students could be asked to make an estimate of the speeds and heights before starting the calculation. Developing a skill and habit for estimation is very useful in more advanced applications of mathematics.

Key questions

  • What has the radius of the earth got to do with this problem?

Possible extension

Try the follow up problem Escape from planet earth .

You could also extend this to suppose that the balls are fired upwards on a trampoline with coefficient of restituion 0.5. How many bounces would it take for each ball to bounce less than 1m high?

Possible support

Provide students with the equation for motion under a constant force.